There are two basic techniques for performing analog-to-digital conversion. An analog-to-digital converter (ADC) using the first technique, known as the open-loop technique, generates a digital signal directly in response to an analog input signal. The open-loop ADC samples the analog input signal at twice the frequency (known as the Nyquist frequency) of the highest expected frequency component of the input signal. The open-loop ADC uses a series of precisely-matched components to digitize the input signal. The resolution and accuracy of the open-loop ADC depend on the matching of these components. However, highly-precise components are difficult to achieve in conventional integrated circuit processing.
An ADC using the second technique, known as the sigma-delta technique, represents the analog input signal by generating a stream of digital samples whise density gives the correct average voltage. The sigma-delta ADC includes a sigma-delta modulator and a decimation filter. The modulator includes a quantizer which generates a digital output signal in response to a filtered difference between the analog input signal and a feedback signal. The feedback signal is the digital output signal reconverted to an analog signal in a digital-to-analog converter (DAC). The modulator is oversampled, meaning that the sampling rate is well above the Nyquist rate. The decimation filter resamples the output of the modulator and provides an N-bit data word at the Nyquist rate. The sigma-delta technique achieves high resolution by precise timing instead of by precisely-matched components (resistors and capacitors) which are required by the open-loop ADC.
A simple sigma-delta ADC uses a first-order modulator with a single integrator performing the filter function, a one-bit quantizer, and a one-bit DAC. Since the quantizer can provide the output of the modulator at only one of two levels, its operation is necessarily linear. The first-order sigma-delta modulator has high quantization noise at the sampling frequency. The action of the filter in the modulator shapes the quantization noise to be higher at higher frequencies. Thus, the converter is referred to as a noise-shaping ADC. The decimation filter has a lowpass characteristic with a cutoff frequency at the Nyquist frequency. Since the sampling frequency is much higher than the Nyquist frequency, the filters can usually attenuate this out-of-band quantization noise sufficiently.
A second-order ADC having two filters in the modulator loop has higher out-of-band quantization noise but lower in-band noise than the first-order ADC. Thus, if the out-of-band noise can be sufficiently filtered, the second-order sigma-delta modulator has better performance. The necessary attenuation can be achieved if the decimation filter is one order greater than the order of the modulator. ADCs higher than second order are possible but typically have stability problems.
One way to increase the resolution of a sigma-delta ADC is to substitute a multi-bit quantizer for the single-bit quantizer. In this case the DAC in the feedback loop must also be multi-bit and the linearity of the multi-bit DAC must be as high as that of the overall ADC. To achieve high DAC linearity, costly error correction techniques are necessary. These error correction techniques would cause the sigma-delta ADC to lose its independence of processing variations. Thus, new techniques are needed to improve the resolution of sigma-delta ADCs.